On the Theory of Surface and Impurity States

A formalism is developed for perturbation theory in which the Hamiltonian is resolved as H = H 0 + V 1 + V 2 and the two perturbing potentials V 1 and V 2 are not treated in a symmetric fashion. All the operators are expressed in the H 0 representation so that the formalism has particular applications in the theory of impurity states and surface and chemisorption states since H 0 can be taken as that part of the Hamiltonian which acts on individual atomic sites, V 1 the interatomic interaction and V 2 , which will have only a small number of non‐zero matrix elements, the effect of the surface or impurity atoms. These applications are illustrated using the linear chain as a model for a one‐dimensional crystal, and the present theory allows the results to be obtained in a very simple way.